Comparisons with experimental measurements \(a_{exp}^l\)  results in studies of the magnetic moments of leptons being a powerful indirect search of new physics. The SM prediction of the anomalous magnetic moment is determined from the sum of all sectors of the
SM which include the QED contributions, the electro-weak contributions, the hadronic vacuum polarization contributions and hadronic light-by-light scattering contributions. The uncertainty of \(a_{SM}\) 
is completely dominated by the hadronic contributions due to the non-perturbative nature of the low energy strong interaction. It is estimated from experimental measurements of the ratio of hadronic to muonic cross sections in electron-positron collisions[1]}. The combined results of muon anomalous magnetic moment in two experiments at FermiLab (FNAL E989)[2]}, and Brookhaven National Laboratory (LabBNL E821) [3]} yield overall deviation from the SM central value:
\(\Delta a_\mu =a^{exp}_\mu -a^{\rm SM}_\mu =(25.1\pm 5.9)\times 10^{-10}, \) 
